Operations Research and Financial Engineering Academic Year 2023 – 2024 Jump To: Jump To: General Information Address Sherrerd Hall Website Department of Operations Research and Financial Engineering Program Offerings: Ph.D. Director of Graduate Studies: Matias Cattaneo Graduate Program Administrator: Kimberly Lupinacci Overview The Operations Research and Financial Engineering (ORFE) department’s intellectual mission is to develop theory and tools in statistics, probability, and optimization to extract meaningful information from data, and to utilize information to make optimal decisions. Faculty and students contribute to both the foundations of these three disciplines and their applications in areas such as data science and machine learning, including deep learning, large-scale optimization, causal inference, biostatistics, policy evaluation, genomics, networks and graphical models, analysis of high-frequency time series and high-dimensional data; decision science, control and learning, including service systems and queues, reinforcement learning, verification and learning of dynamical systems, optimal and stochastic control, robotics and autonomous systems, and large dynamic games. finance and social sciences, including risk management, quantification of model uncertainty, optimal investment, mean field games, optimal contracting, econometrics, causal inference, program evaluation, public policy, decision and choice theory, energy and environmental finance, and reliability management of electricity grids. The department ordinarily offers the Doctor of Philosophy (Ph.D.) in Operations Research and Financial Engineering. This program provide a great deal of flexibility for students in designing individual plans of study and research according to their needs and interests. The department is also a major participant in the Master of Finance (M.Fin.) program offered through the Bendheim Center for Finance. Apply Application deadline January 3, 11:59 p.m. Eastern Standard Time (This deadline is for applications for enrollment beginning in fall 2024) Program length Ph.D. 4 years Fee $75 GRE General Test - optional/not required; Subject Test in Mathematics - optional/not required Additional departmental requirements Applicants are required to select an area of research interest when applying. Program Offerings Ph.D. Program Offering: Ph.D. Courses Courses In consultation with the director of graduate studies, students develop a specific course plan. During the first year, students complete six courses that emphasize the foundations of the program, probability, statistics, and optimization. Students take at least ten courses while enrolled: the six core courses during the first year, two directed research courses, and two additional advanced-level courses in the second year. The following six core courses are required: ORF 522 Linear and Nonlinear Optimization ORF 523 Convex and Conic Optimization ORF 524 Statistical Theory and Methods ORF 525 Statistical Foundations of Data Science ORF 526 Probability Theory ORF 527 Stochastic Calculus In addition, at least two advanced courses and two semesters of directed research (ORF 509 and ORF 510) are completed under the direction of a faculty adviser in the student's area of interest by the end of the second year in preparation for the general examination. Additional pre-generals requirements Additional pre-generals requirements Research Adviser Students ordinarily match with an adviser by the end of the first year of study to begin research in preparation for the general examination. No student may enter the second year without a research adviser of record. Students are expected to identify a faculty adviser in the ORFE department. If a student receives permission to work with a faculty adviser who is not a member of the ORFE department, the student must also have a co-adviser who is on the ORFE faculty and is seriously involved in co-advising the student. Qualifying Examination Each student must satisfy qualifying requirements. Qualifying exams are offered in September of the student’s second year. Each student must satisfy qualifying requirements. Qualifying exams are offered in September of the student’s second year. A student who obtained a grade of A- or better in 4 of the six required classes will be exempt from the qualifying exams. If this is not the case and the student obtained a grade of A- or better in at least 2 of the six required classes, the student will meet with the DGS to decide which exams must be taken to satisfy the requirements. The optimization exams are based on ORF 522 and ORF 523. The statistics exams are based on ORF 524 and ORF 525. The probability exams are based on ORF 526 and ORF 527. If a student received fewer than 2 A- or better grades in the 6 first-year classes, they may not take qualifying exams, and their Ph.D. candidacy ends. The qualifying exams shall not exceed 90 minutes per class, and are administered by 2 ORFE faculty, who will provide the student with the exam questions at least two hours before the examination begins. The examining faculty will decide if the qualifying exam will be written or oral. The results of the qualifying exam(s) are determined by a vote of the faculty. Additional information related to the preliminary examination can be found in the graduate student handbook. General exam General exam ORFE students take the general exam in April or May of their second year. By the end of the Spring semester, students should have met the qualifying examination requirements, have taken and passed ORF 509 and ORF 510, and have passed with a B+ or higher grades two advanced classes. The student must have shown adequate progress in research, and an acceptable level of understanding of their area of specialization. The general exam consists of two parts, a written and an oral part, both covering the student’s primary area of specialization. The written part requires taking and passing, with a B+ or higher grade, two approved advanced classes at the graduate (500) level beyond the 6 core classes counted for the Qualifying Exam. These two classes must be approved by the student’s adviser and the DGS. For each student, an examining committee is selected by the student and adviser. The committee will be approved by the Director of Graduate Studies. Normally, the committee members comprise the student’s adviser(s) and two additional ORFE faculty or associated faculty. The committee will administer the oral exam, evaluate the student’s performance in research and overall knowledge of their field, and make a recommendation to the department faculty. A departmental faculty vote determines the final outcome. The oral exam may be up to 3 hours in length. The general examination committee may ask questions related to the research and the student’s area of specialization. Qualifying for the M.A. Qualifying for the M.A. The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the general examination. It may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met. Please note, students admitted to the Ph.D. program who do not wish to complete the program may be considered for an M.S.E. degree with approval from the department and the Graduate School. Ph.D. students who have already been awarded the incidental M.A. are not eligible to earn an M.S.E. Teaching The department has a teaching requirement of at least a full Assistant in Instruction (AI) assignment or two half AI assignments potentially beginning in the fall of the student's 2nd year depending on the department's teaching needs. Requirements for teaching include: Passing the English Language Proficiency Exam by August after the first year of study (if applicable). Attending the mandatory AI Orientation in fall of the 2nd year of study Dissertation and FPO Dissertation and FPO Upon completion and acceptance of the dissertation by the department, the candidate will be admitted to the final public oral (FPO) examination. The committee of examiners for the FPO must consist of no fewer than two current ORFE faculty members, and the 2nd thesis reader should also be a current ORFE faculty member. The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained. Additional information related to the FPO can be found in the graduate student handbook Faculty Chair Ronnie Sircar Director of Graduate Studies Matias D. Cattaneo Director of Undergraduate Studies Alain L. Kornhauser Professor Amir Ali Ahmadi René A. Carmona Matias D. Cattaneo Jianqing Fan Alain L. Kornhauser Sanjeev R. Kulkarni William A. Massey John M. Mulvey Ronnie Sircar Mete Soner Robert J. Vanderbei Associate Professor Mykhaylo Shkolnikov Ramon van Handel Assistant Professor Boris Hanin Emma Hubert Jason Matthew Klusowski Elizaveta Rebrova Bartolomeo Stellato Ludovic Tangpi Associated Faculty Yacine Aït-Sahalia, Economics Markus K. Brunnermeier, Economics Maria Chudnovsky, Mathematics Filiz Garip, Sociology Elad Hazan, Computer Science H. Vincent Poor, Electrical & Comp Engineering Jennifer Rexford, Provost Paul Seymour, Mathematics Allan M. Sly, Mathematics John D. Storey, Integrative Genomics Rocío Titiunik, Politics Wei Xiong, Economics Lecturer Margaret Holen Daniel Rigobon Daniel Scheinerman Visiting Lecturer Ioannis Akrotirianakis Robert Almgren Alex Dytso Michael Sotiropoulos For a full list of faculty members and fellows please visit the department or program website. Permanent Courses Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students. FIN 501 - Asset Pricing I: Pricing Models and Derivatives (also ORF 514) Provides an introduction of the modern theory of asset pricing. Topics include: (i) no arbitrage, Arrow-Debreu prices and equivalent martingale measure; (ii) security structure and market completeness; (iii) mean-variance analysis, Beta-Pricing, CAPM; and (iv) introduction to derivative pricing. ORF 504 - Financial Econometrics (also FIN 504) This course covers econometric and statistical methods as applied to finance. Topics include: (i) Measurement issues in finance (ii) Predictability of asset returns and volatilities (iii) Value at Risk and extremal events (iv) Linear factor pricing and portfolio problems (v) Intertemporal models of the Stochastic Discount Factor and Generalized Method of Moments (vi) Vector Autoregressive and maximum likelihood methods in finance (vii) Risk Neutral valuation in discrete time (viii) Estimation methods for continuous time models (ix) Volatility smiles and alternatives to Black-Scholes (x) Nonparametric statistical methods for option pricing. ORF 505 - Statistical Analysis of Financial Data (also FIN 505) Linear and mixed effect models. Nonlinear regression. Nonparametricegression and classification. Time series analysis: stationarity and classical linear models (AR, MA, ARMA, ..). Nonlinear and nonstationary time series models. State space systems, hidden Markov models and filtering. ORF 509 - Directed Research I Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 one semester prior to taking the general examination. ORF 510 - Directed Research II Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 one semester prior to taking the general examination. ORF 511 - Extramural Summer Project Summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor, that will provide practical experience relevant to the student's course of study. Start date no earlier than June 1. A research report and sponsor's evaluation are required. ORF 515 - Asset Pricing II: Stochastic Calculus and Advanced Derivatives (also FIN 503) Course begins with an overview of basic probability theory and covers the elements of stochastic calculus and stochastic differential equations that are widely used in modern financial applications. Topics include the Poisson process, Brownian motion, martingales, diffusions and their connection with partial differential equations. Examples from applications include the Black-Scholes option pricing and hedging theory, bond pricing and stochastic volatility models. ORF 522 - Linear and Nonlinear Optimization Theoretical concepts underlying linear programming, with computer implementations of some of the different methods. The topics covered include duality theory, the simplex method, interior point methods, related numerical issues, and modeling paradigms. ORF 523 - Convex and Conic Optimization An introduction to the central concepts needed for studying the theory, algorithms, and applications of nonlinear optimization problems. Topics covered include first- and second-order optimality conditions; unconstrained methods, including steepest descent, conjugate gradient, and quasi-Newtonian methods; constrained active-set methods; and duality theory and Lagrangian methods. Prerequisite: linear optimization. ORF 524 - Statistical Theory and Methods A graduate level introduction to statistical theory and methods. It introduces some of the most important and commonly-used principles of statistical inference and covers the statistical theory and methods for point estimation, confidence intervals, and hypothesis testing, and the applications of the fundamental theory to linear models and categorical data. ORF 525 - Statistical Foundations of Data Science An introduction to the most important and broadly utilized statistical methods used in many scienti¿c data analysis, including general linear, mixed-e¿ects, generalized linear models, regression and ANOVA models. The methodological power of statistics will be emphasized. Objectives of this course are to give students a solid understanding of these methods, and o¿er them experience in applying these methods to real data using statistical computing packages and interpreting results. For master's/Ph.D. students and advanced undergraduates. ORF 526 - Probability Theory Graduate introduction to probability theory beginning with a review of measure and integration. Topics include random variables, expectation, characteristic functions, law of large numbers, central limit theorem, conditioning, martin- gales, Markov chains, and Poisson processes. ORF 527 - Stochastic Calculus An introduction to stochastic analysis based on Brownian motion. Topics include local martingales, the Ito integral and calculus, stochastic differential equations, the Feynman-Kac formula, representation theorems, Girsanov theory, and applications in finance. ORF 531 - Computational Finance in C++ (also FIN 531) Introduce the student to the technical and algorithmic aspects of a wide spectrum of computer applications currently used in the financial industry, and to prepare the student for the development of new applications. The student will be introduced to C++, the weekly homework will involve writing C++ code, and the final project will also involve programming in the same environment. ORF 535 - Financial Risk and Wealth Management (also FIN 535) This course is about measuring, modeling and managing financial risks. It introduces the variety of instruments that are used to this effect and the methods of designing and evaluating such instruments. Topics covered include risk diversification, planning models, market and nonmarket risks, and portfolio effects. Lectures meet concurrently with ORF 435. Credit for graduate course requires completion of additional assignments. ORF 538 - PDE Methods for Financial Mathematics An introduction to analytical and computational methods common to financial engineering problems. Aimed at PhD students and advanced masters students who have studied stochastic calculus, the course focuses on uses of partial differential equations: their appearance in pricing financial derivatives, their connection with Markov processes, their occurrence as Hamilton-Jacobi-Bellman equations in stochastic control problems, and analytical, asymptotic, and numerical techniques for their solution. ORF 542 - Stochastic Optimal Control Deterministic optimal control, dynamic programming, and Pontryagin maximum principle. Controlled diffusion processes and stochastic dynamic programming. Hamilton-Jacobi-Bellman equation, viscosity solutions. Merton problem, singular optimal control, option pricing via utility maximization. ORF 543 - Deep Learning Theory This course is an introduction to deep learning theory. Using tools from mathematics (e.g. probability, functional analysis, spectral asymptotics and combinatorics) as well as physics (e.g. effective field theory, the 1/n expansion, and the renormalization group) we cover topics in approximation theory, optimization, and generalization. ORF 544 - Stochastic Optimization This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such as reinforcement learning and approximate dynamic programming. Also covered are both offline and online learning problems. Considerable emphasis is placed on modeling and computation. ORF 545 - High Frequency Markets: Models and Data Analysis (also FIN 545) An introduction to the microstructure of modern electronic financial markets and high frequency trading strategies. Topics include market structure and optimization techniques used by various market participants, tools for analyzing limit order books at high frequency, and stochastic dynamic optimization strategies for trading with minimal market impact at high and medium frequency. The course makes essential use of high-frequency futures data, accessed using the Kdb+ database language. Graduate credit requires completion of extended and more sophisticated homework assignments. ORF 550 - Topics in Probability (also APC 550) An introduction to nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics. Emphasis is on developing a common set of tools that has proved to be useful in different areas. Topics may include: concentration of measure; functional, transportation cost, martingale inequalities; isoperimetry; Markov semigroups, mixing times, random fields; hypercontractivity; thresholds and influences; Stein's method; suprema of random processes; Gaussian and Rademacher inequalities; generic chaining; entropy and combinatorial dimensions; selected applications. ORF 569 - Special Topics in Statistics, Operations Research and Financial Engineering Advanced topics in statistics and operations research or the investigation of problems of current interest. ORF 570 - Special Topics in Statistics and Operations Research (also ECE 578) Advanced topics in statistics and operations research or the investigation of problems of current interest. ORF 574 - Special Topics in Investment Science (also FIN 574) Emphasis on quantitative analysis of markets, trading strategies, risk and return profiles and portfolio analysis. Students develop portfolios of hedge funds; analyze trading models for various hedge fund styles; develop Value-at-Risk analysis of various trading systems and portfolios; analyze relationship between macro-economic variables and various hedge fund trading strategies; analyze hedge funds from the standpoint of asset allocation and efficient frontier models. We will also bring in experts and practitioners in a number of hedge fund trading strategies to add industry feel and context to the lectures and exercises.
